/*  Correct the extracted line width and position; part of detect-lines.
    Copyright (C) 1996-1998 Carsten Steger

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2, or (at your option)
    any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program; if not, write to the Free Software
    Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */



#include "lines.h"



/* Macros */

/* interpolate bilinearly between i_re and i_re+1 with parameter a and between
   i_we and i_we+1 with parameter b on the member field in the correction
   table. */
#define BILINEAR(a,b,field) \
  ((1-b)*((1-a)*ctable[i_re][i_we].field+a*ctable[i_re][i_we+1].field)+ \
   b*((1-a)*ctable[i_re+1][i_we].field+a*ctable[i_re+1][i_we+1].field))



/* Type declarations */

/* This structure holds the information about the true line width w and
   asymmetry h, and the line position correction for the values of w_est (total
   line width) and r_est (gradient ratio) that can be extracted from the image.
   Currently, the table is sampled at uniform values from [2,6]x[0,1], so w_est
   and r_est could be omitted from the table.  However, future versions of the
   algorithm might use irregularly sampled w_est and r_est.  Therefore, they
   are contained in the structure.  The structure also contains the true line
   width on the strong and weak side of the line, as measured by the gradient.
   These values could be used to check whether the extracted line conforms to
   the line model, but the current implementation use this information.
   However, future versions of the algorithm might do this.  Finally, the
   entry is_valid contains a flag whether the table entry is valid or not,
   since some combinations of w_est and r_est cannot occur.  Again, this could
   be used to check whether the model assumptions are fulfilled. */
struct correction {
  double w_est;       /* Total line width extracted from the image */
  double r_est;       /* Gradient ratio extracted from the image */
  double w;           /* True line width */
  double h;           /* True asymmetry */
  double correction;  /* Line position correction */
  double w_strong;    /* True width on the side with the stronger gradient */
  double w_weak;      /* True width on the side with the weaker gradient */
  bool   is_valid;    /* Is this table entry valid? */
};



/* Table of the line width and position corrections.  This table is sampled at
   41 uniform values for w_est in [2,6] and 21 uniform values for r_est in
   [0,1]. */
correction ctable[21][41] = {
  {
    {2.0, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.2, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.3, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.4, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.5, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.6, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.7, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.8, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.9, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.0, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.1, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.2, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.3, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.4, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.5, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.6, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.7, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.8, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {3.9, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.0, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.1, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.2, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.3, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.4, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.5, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.6, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.7, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.8, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {4.9, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.0, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.1, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.2, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.3, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.4, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.5, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.6, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.7, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.8, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {5.9, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {6.0, 0.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0}
  },
  {
    {2.0, 0.05, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.05, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.2, 0.05, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.3, 0.05, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.4, 0.05, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.5, 0.05, 0.39451193, 0.65711873, 1.35657624, 1.96381471, 0.53618529, 1},
    {2.6, 0.05, 0.63729269, 0.80935336, 1.30029235, 2.03985229, 0.56014771, 1},
    {2.7, 0.05, 0.81466418, 0.86836672, 1.24452224, 2.11300616, 0.58699384, 1},
    {2.8, 0.05, 0.96412770, 0.89909203, 1.18944119, 2.18266521, 0.61733479, 1},
    {2.9, 0.05, 1.09676455, 0.91717245, 1.13561041, 2.24831390, 0.65168610, 1},
    {3.0, 0.05, 1.21692489, 0.92848988, 1.08384513, 2.30961284, 0.69038716, 1},
    {3.1, 0.05, 1.32646409, 0.93580164, 1.03499886, 2.36645213, 0.73354787, 1},
    {3.2, 0.05, 1.42633569, 0.94059785, 0.98974767, 2.41895971, 0.78104029, 1},
    {3.3, 0.05, 1.51730916, 0.94376456, 0.94845804, 2.46746712, 0.83253288, 1},
    {3.4, 0.05, 1.60025122, 0.94586075, 0.91116814, 2.51245011, 0.88754989, 1},
    {3.5, 0.05, 1.67616918, 0.94725013, 0.87765423, 2.55446371, 0.94553629, 1},
    {3.6, 0.05, 1.74614708, 0.94817227, 0.84753168, 2.59408497, 1.00591503, 1},
    {3.7, 0.05, 1.81125741, 0.94878534, 0.82034984, 2.63186937, 1.06813063, 1},
    {3.8, 0.05, 1.87248943, 0.94919364, 0.79566103, 2.66832172, 1.13167828, 1},
    {3.9, 0.05, 1.93070645, 0.94946590, 0.77306078, 2.70388005, 1.19611995, 1},
    {4.0, 0.05, 1.98662965, 0.94964748, 0.75220527, 2.73890956, 1.26109044, 1},
    {4.1, 0.05, 2.04084073, 0.94976843, 0.73281358, 2.77370375, 1.32629625, 1},
    {4.2, 0.05, 2.09379566, 0.94984878, 0.71466202, 2.80849036, 1.39150964, 1},
    {4.3, 0.05, 2.14584335, 0.94990193, 0.69757485, 2.84343972, 1.45656028, 1},
    {4.4, 0.05, 2.19724527, 0.94993688, 0.68141474, 2.87867411, 1.52132589, 1},
    {4.5, 0.05, 2.24819385, 0.94995971, 0.66607397, 2.91427698, 1.58572302, 1},
    {4.6, 0.05, 2.29882832, 0.94997451, 0.65146721, 2.95030144, 1.64969856, 1},
    {4.7, 0.05, 2.34924790, 0.94998402, 0.63752588, 2.98677756, 1.71322244, 1},
    {4.8, 0.05, 2.39952228, 0.94999007, 0.62419378, 3.02371845, 1.77628155, 1},
    {4.9, 0.05, 2.44969972, 0.94999389, 0.61142395, 3.06112517, 1.83887483, 1},
    {5.0, 0.05, 2.49981321, 0.94999628, 0.59917634, 3.09899049, 1.90100951, 1},
    {5.1, 0.05, 2.54988502, 0.94999776, 0.58741617, 3.13730176, 1.96269824, 1},
    {5.2, 0.05, 2.59992995, 0.94999866, 0.57611272, 3.17604302, 2.02395698, 1},
    {5.3, 0.05, 2.64995776, 0.94999921, 0.56523852, 3.21519649, 2.08480351, 1},
    {5.4, 0.05, 2.69997480, 0.94999954, 0.55476869, 3.25474362, 2.14525638, 1},
    {5.5, 0.05, 2.74998512, 0.94999973, 0.54468056, 3.29466575, 2.20533425, 1},
    {5.6, 0.05, 2.79999130, 0.94999985, 0.53495330, 3.33494464, 2.26505536, 1},
    {5.7, 0.05, 2.84999497, 0.94999991, 0.52556769, 3.37556268, 2.32443732, 1},
    {5.8, 0.05, 2.89999712, 0.94999995, 0.51650591, 3.41650304, 2.38349696, 1},
    {5.9, 0.05, 2.94999837, 0.94999997, 0.50775142, 3.45774980, 2.44225020, 1},
    {6.0, 0.05, 2.99999908, 0.94999998, 0.49928881, 3.49928790, 2.50071210, 1}
  },
  {
    {2.0, 0.10, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.10, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.2, 0.10, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.3, 0.10, 0.21877029, 0.37919742, 1.08959528, 1.70353792, 0.59646208, 1},
    {2.4, 0.10, 0.55321986, 0.68457297, 1.04282943, 1.77631890, 0.62368110, 1},
    {2.5, 0.10, 0.74830067, 0.77538178, 0.99782962, 1.84682624, 0.65317376, 1},
    {2.6, 0.10, 0.90103267, 0.82093886, 0.95447592, 1.91457985, 0.68542015, 1},
    {2.7, 0.10, 1.03086984, 0.84772552, 0.91285559, 1.97916489, 0.72083511, 1},
    {2.8, 0.10, 1.14549804, 0.86473351, 0.87320467, 2.04028418, 0.75971582, 1},
    {2.9, 0.10, 1.24865758, 0.87597877, 0.83581862, 2.09779835, 0.80220165, 1},
    {3.0, 0.10, 1.34244262, 0.88357147, 0.80095702, 2.15174175, 0.84825825, 1},
    {3.1, 0.10, 1.42823493, 0.88874994, 0.76877227, 2.20231067, 0.89768933, 1},
    {3.2, 0.10, 1.50712643, 0.89229689, 0.73927998, 2.24982998, 0.95017002, 1},
    {3.3, 0.10, 1.58009750, 0.89472991, 0.71236930, 2.29470881, 1.00529119, 1},
    {3.4, 0.10, 1.64807137, 0.89639940, 0.68783797, 2.33739605, 1.06260395, 1},
    {3.5, 0.10, 1.71191250, 0.89754487, 0.66543423, 2.37834252, 1.12165748, 1},
    {3.6, 0.10, 1.77240775, 0.89833050, 0.64489333, 2.41797285, 1.18202715, 1},
    {3.7, 0.10, 1.83024928, 0.89886882, 0.62596303, 2.45666745, 1.24333255, 1},
    {3.8, 0.10, 1.88602625, 0.89923705, 0.60841798, 2.49475308, 1.30524692, 1},
    {3.9, 0.10, 1.94022542, 0.89948824, 0.59206537, 2.53250020, 1.36749980, 1},
    {4.0, 0.10, 1.99323862, 0.89965892, 0.57674481, 2.57012499, 1.42987501, 1},
    {4.1, 0.10, 2.04537405, 0.89977429, 0.56232516, 2.60779445, 1.49220555, 1},
    {4.2, 0.10, 2.09686919, 0.89985181, 0.54870000, 2.64563288, 1.55436712, 1},
    {4.3, 0.10, 2.14790373, 0.89990351, 0.53578302, 2.68372903, 1.61627097, 1},
    {4.4, 0.10, 2.19861130, 0.89993773, 0.52350376, 2.72214290, 1.67785710, 1},
    {4.5, 0.10, 2.24908973, 0.89996017, 0.51180415, 2.76091205, 1.73908795, 1},
    {4.6, 0.10, 2.29940959, 0.89997477, 0.50063564, 2.80005699, 1.79994301, 1},
    {4.7, 0.10, 2.34962106, 0.89998416, 0.48995704, 2.83958563, 1.86041437, 1},
    {4.8, 0.10, 2.39975932, 0.89999016, 0.47973283, 2.87949693, 1.92050307, 1},
    {4.9, 0.10, 2.44984872, 0.89999394, 0.46993198, 2.91978370, 1.98021630, 1},
    {5.0, 0.10, 2.49990590, 0.89999631, 0.46052697, 2.96043474, 2.03956526, 1},
    {5.1, 0.10, 2.54994208, 0.89999777, 0.45149316, 3.00143639, 2.09856361, 1},
    {5.2, 0.10, 2.59996471, 0.89999867, 0.44280828, 3.04277369, 2.15722631, 1},
    {5.3, 0.10, 2.64997872, 0.89999921, 0.43445202, 3.08443117, 2.21556883, 1},
    {5.4, 0.10, 2.69998730, 0.89999954, 0.42640580, 3.12639335, 2.27360665, 1},
    {5.5, 0.10, 2.74999250, 0.89999973, 0.41865249, 3.16864514, 2.33135486, 1},
    {5.6, 0.10, 2.79999562, 0.89999985, 0.41117628, 3.21117198, 2.38882802, 1},
    {5.7, 0.10, 2.84999746, 0.89999991, 0.40396250, 3.25396002, 2.44603998, 1},
    {5.8, 0.10, 2.89999855, 0.89999995, 0.39699754, 3.29699612, 2.50300388, 1},
    {5.9, 0.10, 2.94999918, 0.89999997, 0.39026872, 3.34026792, 2.55973208, 1},
    {6.0, 0.10, 2.99999954, 0.89999998, 0.38376422, 3.38376376, 2.61623624, 1}
  },
  {
    {2.0, 0.15, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.15, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.2, 0.15, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.3, 0.15, 0.51495761, 0.59473282, 0.87697386, 1.62862197, 0.67137803, 1},
    {2.4, 0.15, 0.72159043, 0.70188701, 0.83862164, 1.69671098, 0.70328902, 1},
    {2.5, 0.15, 0.87668389, 0.75502109, 0.80221797, 1.76246497, 0.73753503, 1},
    {2.6, 0.15, 1.00530865, 0.78637591, 0.76769330, 1.82553960, 0.77446040, 1},
    {2.7, 0.15, 1.11703187, 0.80644909, 0.73507961, 1.88568549, 0.81431451, 1},
    {2.8, 0.15, 1.21658884, 0.81986940, 0.70445867, 1.94277809, 0.85722191, 1},
    {2.9, 0.15, 1.30669230, 0.82905423, 0.67590851, 1.99683071, 0.90316929, 1},
    {3.0, 0.15, 1.38910244, 0.83541673, 0.64946205, 2.04798808, 0.95201192, 1},
    {3.1, 0.15, 1.46510896, 0.83984926, 0.62508653, 2.09650320, 1.00349680, 1},
    {3.2, 0.15, 1.53575726, 0.84294409, 0.60268425, 2.14270447, 1.05729553, 1},
    {3.3, 0.15, 1.60194844, 0.84510584, 0.58210775, 2.18696061, 1.11303939, 1},
    {3.4, 0.15, 1.66447712, 0.84661499, 0.56318110, 2.22964917, 1.17035083, 1},
    {3.5, 0.15, 1.72404185, 0.84766724, 0.54571992, 2.27113192, 1.22886808, 1},
    {3.6, 0.15, 1.78124688, 0.84839950, 0.52954661, 2.31173802, 1.28826198, 1},
    {3.7, 0.15, 1.83660380, 0.84890765, 0.51449966, 2.35175431, 1.34824569, 1},
    {3.8, 0.15, 1.89053617, 0.84925898, 0.50043792, 2.39142152, 1.40857848, 1},
    {3.9, 0.15, 1.94338714, 0.84950072, 0.48724130, 2.43093478, 1.46906522, 1},
    {4.0, 0.15, 1.99542913, 0.84966610, 0.47480926, 2.47044699, 1.52955301, 1},
    {4.1, 0.15, 2.04687439, 0.84977849, 0.46305830, 2.51007378, 1.58992622, 1},
    {4.2, 0.15, 2.09788538, 0.84985430, 0.45191914, 2.54989923, 1.65010077, 1},
    {4.3, 0.15, 2.14858449, 0.84990501, 0.44133403, 2.58998156, 1.71001844, 1},
    {4.4, 0.15, 2.19906243, 0.84993863, 0.43125446, 2.63035849, 1.76964151, 1},
    {4.5, 0.15, 2.24938551, 0.84996073, 0.42163920, 2.67105190, 1.82894810, 1},
    {4.6, 0.15, 2.29960147, 0.84997511, 0.41245278, 2.71207185, 1.88792815, 1},
    {4.7, 0.15, 2.34974423, 0.84998437, 0.40366432, 2.75341983, 1.94658017, 1},
    {4.8, 0.15, 2.39983755, 0.84999029, 0.39524659, 2.79509131, 2.00490869, 1},
    {4.9, 0.15, 2.44989790, 0.84999402, 0.38717534, 2.83707774, 2.06292226, 1},
    {5.0, 0.15, 2.49993649, 0.84999636, 0.37942878, 2.87936807, 2.12063193, 1},
    {5.1, 0.15, 2.54996091, 0.84999780, 0.37198714, 2.92194977, 2.17805023, 1},
    {5.2, 0.15, 2.59997618, 0.84999869, 0.36483242, 2.96480966, 2.23519034, 1},
    {5.3, 0.15, 2.64998564, 0.84999922, 0.35794813, 3.00793440, 2.29206560, 1},
    {5.4, 0.15, 2.69999143, 0.84999954, 0.35131907, 3.05131088, 2.34868912, 1},
    {5.5, 0.15, 2.74999494, 0.84999974, 0.34493122, 3.09492638, 2.40507362, 1},
    {5.6, 0.15, 2.79999704, 0.84999985, 0.33877160, 3.13876878, 2.46123122, 1},
    {5.7, 0.15, 2.84999829, 0.84999991, 0.33282817, 3.18282653, 2.51717347, 1},
    {5.8, 0.15, 2.89999902, 0.84999995, 0.32708971, 3.22708877, 2.57291123, 1},
    {5.9, 0.15, 2.94999944, 0.84999997, 0.32154579, 3.27154526, 2.62845474, 1},
    {6.0, 0.15, 2.99999969, 0.84999999, 0.31618668, 3.31618638, 2.68381362, 1}
  },
  {
    {2.0, 0.20, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.20, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.2, 0.20, 0.37590631, 0.43802047, 0.76653390, 1.50171448, 0.69828552, 1},
    {2.3, 0.20, 0.63559658, 0.60584521, 0.73239191, 1.56839938, 0.73160062, 1},
    {2.4, 0.20, 0.80878262, 0.67788209, 0.70033504, 1.63318175, 0.76681825, 1},
    {2.5, 0.20, 0.94582063, 0.71853708, 0.67018762, 1.69574617, 0.80425383, 1},
    {2.6, 0.20, 1.06169829, 0.74408983, 0.64186257, 1.75584733, 0.84415267, 1},
    {2.7, 0.20, 1.16325725, 0.76106674, 0.61532865, 1.81333658, 0.88666342, 1},
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    {3.6, 0.20, 1.78563151, 0.79845154, 0.44850391, 2.23535435, 1.36464565, 1},
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    {3.9, 0.20, 1.94494772, 0.79951258, 0.41312261, 2.35847367, 1.54152633, 1},
    {4.0, 0.20, 1.99650948, 0.79967348, 0.40265439, 2.39943952, 1.60056048, 1},
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    {5.9, 0.20, 2.94999958, 0.79999997, 0.27278610, 3.22278571, 2.67721429, 1},
    {6.0, 0.20, 2.99999976, 0.79999999, 0.26823966, 3.26823944, 2.73176056, 1}
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  {
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  },
  {
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  },
  {
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    {5.7, 0.35, 2.84999919, 0.64999992, 0.18417933, 3.03417870, 2.66582130, 1},
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    {5.9, 0.35, 2.94999974, 0.64999998, 0.17793596, 3.12793575, 2.77206425, 1},
    {6.0, 0.35, 2.99999985, 0.64999999, 0.17497036, 3.17497024, 2.82502976, 1}
  },
  {
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    {2.1, 0.40, 0.37456090, 0.28275455, 0.44363568, 1.28245932, 0.81754068, 1},
    {2.2, 0.40, 0.63912110, 0.41788353, 0.42330376, 1.34256272, 0.85743728, 1},
    {2.3, 0.40, 0.81053189, 0.48100260, 0.40458396, 1.40149073, 0.89850927, 1},
    {2.4, 0.40, 0.94330141, 0.51841224, 0.38729233, 1.45906826, 0.94093174, 1},
    {2.5, 0.40, 1.05367129, 0.54270452, 0.37128539, 1.51516543, 0.98483457, 1},
    {2.6, 0.40, 1.14921427, 0.55924766, 0.35644883, 1.56970904, 1.03029096, 1},
    {2.7, 0.40, 1.23420161, 0.57082520, 0.34268752, 1.62268813, 1.07731187, 1},
    {2.8, 0.40, 1.31132809, 0.57905816, 0.32991766, 1.67415274, 1.12584726, 1},
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    {3.9, 0.40, 1.94717224, 0.59957718, 0.23501625, 2.18298001, 1.71701999, 1},
    {4.0, 0.40, 1.99804848, 0.59971605, 0.22911884, 2.22771125, 1.77228875, 1},
    {4.1, 0.40, 2.04866701, 0.59981104, 0.22351569, 2.27255308, 1.82744692, 1},
    {4.2, 0.40, 2.09909888, 0.59987543, 0.21818395, 2.31753265, 1.88246735, 1},
    {4.3, 0.40, 2.14939712, 0.59991865, 0.21310333, 2.36266734, 1.93733266, 1},
    {4.4, 0.40, 2.19960083, 0.59994739, 0.20825579, 2.40796699, 1.99203301, 1},
    {4.5, 0.40, 2.24973845, 0.59996631, 0.20362511, 2.45343583, 2.04656417, 1},
    {4.6, 0.40, 2.29983040, 0.59997863, 0.19919671, 2.49907395, 2.10092605, 1},
    {4.7, 0.40, 2.34989116, 0.59998658, 0.19495737, 2.54487857, 2.15512143, 1},
    {4.8, 0.40, 2.39993088, 0.59999166, 0.19089505, 2.59084501, 2.20915499, 1},
    {4.9, 0.40, 2.44995656, 0.59999486, 0.18699880, 2.63696735, 2.26303265, 1},
    {5.0, 0.40, 2.49997298, 0.59999687, 0.18325856, 2.68323900, 2.31676100, 1},
    {5.1, 0.40, 2.54998337, 0.59999811, 0.17966510, 2.72965305, 2.37034695, 1},
    {5.2, 0.40, 2.59998987, 0.59999887, 0.17620990, 2.77620256, 2.42379744, 1},
    {5.3, 0.40, 2.64999389, 0.59999933, 0.17288513, 2.82288070, 2.47711930, 1},
    {5.4, 0.40, 2.69999635, 0.59999961, 0.16968352, 2.86968088, 2.53031912, 1},
    {5.5, 0.40, 2.74999785, 0.59999977, 0.16659834, 2.91659678, 2.58340322, 1},
    {5.6, 0.40, 2.79999874, 0.59999987, 0.16362336, 2.96362245, 2.63637755, 1},
    {5.7, 0.40, 2.84999927, 0.59999993, 0.16075277, 3.01075224, 2.68924776, 1},
    {5.8, 0.40, 2.89999958, 0.59999996, 0.15798117, 3.05798086, 2.74201914, 1},
    {5.9, 0.40, 2.94999976, 0.59999998, 0.15530352, 3.10530335, 2.79469665, 1},
    {6.0, 0.40, 2.99999987, 0.59999999, 0.15271512, 3.15271503, 2.84728497, 1}
  },
  {
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    {2.8, 0.45, 1.31722136, 0.53041163, 0.28692929, 1.63967412, 1.16032588, 1},
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    {3.0, 0.45, 1.45245568, 0.53987437, 0.26722183, 1.73841714, 1.26158286, 1},
    {3.1, 0.45, 1.51432639, 0.54275120, 0.25837482, 1.78630380, 1.31369620, 1},
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    {3.3, 0.45, 1.63039298, 0.54633690, 0.24239568, 1.87990181, 1.42009819, 1},
    {3.4, 0.45, 1.68565300, 0.54741860, 0.23515743, 1.92592296, 1.47407704, 1},
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    {3.6, 0.45, 1.79253049, 0.54874453, 0.22195484, 2.01708113, 1.58291887, 1},
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    {3.8, 0.45, 1.89625977, 0.54940826, 0.21020157, 2.10774212, 1.69225788, 1},
    {3.9, 0.45, 1.94739281, 0.54959892, 0.20479094, 2.15307233, 1.74692767, 1},
    {4.0, 0.45, 1.99820102, 0.54973058, 0.19965688, 2.19846890, 1.80153110, 1},
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    {5.6, 0.45, 2.79999884, 0.54999988, 0.14259067, 2.94258990, 2.65741010, 1},
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    {5.8, 0.45, 2.89999962, 0.54999996, 0.13767374, 3.03767349, 2.76232651, 1},
    {5.9, 0.45, 2.94999978, 0.54999998, 0.13534029, 3.08534014, 2.81465986, 1},
    {6.0, 0.45, 2.99999988, 0.54999999, 0.13308462, 3.13308454, 2.86691546, 1}
  },
  {
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    {2.8, 0.50, 1.32170772, 0.48179260, 0.24868574, 1.60856389, 1.19143611, 1},
    {2.9, 0.50, 1.39061051, 0.48687002, 0.23990401, 1.65840363, 1.24159637, 1},
    {3.0, 0.50, 1.45520527, 0.49055260, 0.23172974, 1.70730505, 1.29269495, 1},
    {3.1, 0.50, 1.51644027, 0.49322635, 0.22410735, 1.75540106, 1.34459894, 1},
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    {3.3, 0.50, 1.63159652, 0.49656872, 0.21031794, 1.84973546, 1.45026454, 1},
    {3.4, 0.50, 1.68654452, 0.49757976, 0.20406173, 1.89624161, 1.50375839, 1},
    {3.5, 0.50, 1.74025100, 0.49830468, 0.19817896, 1.94246628, 1.55753372, 1},
    {3.6, 0.50, 1.79300246, 0.49882135, 0.19263572, 1.98850956, 1.61149044, 1},
    {3.7, 0.50, 1.84502555, 0.49918708, 0.18740192, 2.03445477, 1.66554523, 1},
    {3.8, 0.50, 1.89649836, 0.49944402, 0.18245095, 2.08036902, 1.71963098, 1},
    {3.9, 0.50, 1.94755963, 0.49962306, 0.17775928, 2.12630453, 1.77369547, 1},
    {4.0, 0.50, 1.99831638, 0.49974675, 0.17330609, 2.17230053, 1.82769947, 1},
    {4.1, 0.50, 2.04885027, 0.49983142, 0.16907289, 2.21838525, 1.88161475, 1},
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    {4.4, 0.50, 2.19965583, 0.49995304, 0.15753675, 2.35733046, 2.04266954, 1},
    {4.5, 0.50, 2.24977450, 0.49996992, 0.15403478, 2.40389957, 2.09610043, 1},
    {4.6, 0.50, 2.29985378, 0.49998092, 0.15068545, 2.45059776, 2.14940224, 1},
    {4.7, 0.50, 2.34990617, 0.49998802, 0.14747891, 2.49742263, 2.20257737, 1},
    {4.8, 0.50, 2.39994041, 0.49999255, 0.14440614, 2.54437040, 2.25562960, 1},
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    {5.6, 0.50, 2.79999892, 0.49999988, 0.12377629, 2.92377564, 2.67622436, 1},
    {5.7, 0.50, 2.84999937, 0.49999993, 0.12160477, 2.97160440, 2.72839560, 1},
    {5.8, 0.50, 2.89999964, 0.49999996, 0.11950814, 3.01950792, 2.78049208, 1},
    {5.9, 0.50, 2.94999980, 0.49999998, 0.11748257, 3.06748245, 2.83251755, 1},
    {6.0, 0.50, 2.99999989, 0.49999999, 0.11552453, 3.11552446, 2.88447554, 1}
  },
  {
    {2.0, 0.55, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.55, 0.47169642, 0.23701703, 0.28675177, 1.20446254, 0.89553746, 1},
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    {2.6, 0.55, 1.17086826, 0.41785174, 0.23103800, 1.47783911, 1.12216089, 1},
    {2.7, 0.55, 1.25157764, 0.42679344, 0.22232306, 1.52952634, 1.17047366, 1},
    {2.8, 0.55, 1.32515949, 0.43322418, 0.21423513, 1.58023236, 1.21976764, 1},
    {2.9, 0.55, 1.39332559, 0.43788252, 0.20671565, 1.63003426, 1.26996574, 1},
    {3.0, 0.55, 1.45731642, 0.44126869, 0.19971180, 1.67903292, 1.32096708, 1},
    {3.1, 0.55, 1.51806205, 0.44373207, 0.19317564, 1.72734378, 1.37265622, 1},
    {3.2, 0.55, 1.57627695, 0.44552194, 0.18706359, 1.77508788, 1.42491212, 1},
    {3.3, 0.55, 1.63251889, 0.44681879, 0.18133623, 1.82238420, 1.47761580, 1},
    {3.4, 0.55, 1.68722751, 0.44775453, 0.17595809, 1.86934387, 1.53065613, 1},
    {3.5, 0.55, 1.74075075, 0.44842620, 0.17089742, 1.91606622, 1.58393378, 1},
    {3.6, 0.55, 1.79336388, 0.44890533, 0.16612598, 1.96263679, 1.63736321, 1},
    {3.7, 0.55, 1.84528394, 0.44924473, 0.16161869, 2.00912666, 1.69087334, 1},
    {3.8, 0.55, 1.89668102, 0.44948331, 0.15735329, 2.05559295, 1.74440705, 1},
    {3.9, 0.55, 1.94768732, 0.44964963, 0.15331007, 2.10208007, 1.79791993, 1},
    {4.0, 0.55, 1.99840468, 0.44976456, 0.14947148, 2.14862129, 1.85137871, 1},
    {4.1, 0.55, 2.04891066, 0.44984326, 0.14582189, 2.19524051, 1.90475949, 1},
    {4.2, 0.55, 2.09926376, 0.44989663, 0.14234731, 2.24195396, 1.95804604, 1},
    {4.3, 0.55, 2.14950751, 0.44993249, 0.13903516, 2.28877185, 2.01122815, 1},
    {4.4, 0.55, 2.19967396, 0.44995633, 0.13587414, 2.33569973, 2.06430027, 1},
    {4.5, 0.55, 2.24978638, 0.44997203, 0.13285398, 2.38273967, 2.11726033, 1},
    {4.6, 0.55, 2.29986149, 0.44998226, 0.12996538, 2.42989124, 2.17010876, 1},
    {4.7, 0.55, 2.34991112, 0.44998886, 0.12719986, 2.47715228, 2.22284772, 1},
    {4.8, 0.55, 2.39994356, 0.44999307, 0.12454968, 2.52451946, 2.27548054, 1},
    {4.9, 0.55, 2.44996452, 0.44999574, 0.12200774, 2.57198874, 2.32801126, 1},
    {5.0, 0.55, 2.49997793, 0.44999740, 0.11956751, 2.61955570, 2.38044430, 1},
    {5.1, 0.55, 2.54998642, 0.44999843, 0.11722301, 2.66721573, 2.43278427, 1},
    {5.2, 0.55, 2.59999173, 0.44999906, 0.11496869, 2.71496426, 2.48503574, 1},
    {5.3, 0.55, 2.64999501, 0.44999945, 0.11279946, 2.76279678, 2.53720322, 1},
    {5.4, 0.55, 2.69999702, 0.44999968, 0.11071057, 2.81070897, 2.58929103, 1},
    {5.5, 0.55, 2.74999824, 0.44999981, 0.10869764, 2.85869670, 2.64130330, 1},
    {5.6, 0.55, 2.79999897, 0.44999989, 0.10675661, 2.90675606, 2.69324394, 1},
    {5.7, 0.55, 2.84999941, 0.44999994, 0.10488369, 2.95488337, 2.74511663, 1},
    {5.8, 0.55, 2.89999966, 0.44999997, 0.10307535, 3.00307516, 2.79692484, 1},
    {5.9, 0.55, 2.94999981, 0.44999998, 0.10132831, 3.05132820, 2.84867180, 1},
    {6.0, 0.55, 2.99999989, 0.44999999, 0.09963950, 3.09963944, 2.90036056, 1}
  },
  {
    {2.0, 0.60, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.60, 0.48906653, 0.21274038, 0.24454465, 1.18247100, 0.91752900, 1},
    {2.2, 0.60, 0.70777594, 0.28134519, 0.23338893, 1.23800321, 0.96199679, 1},
    {2.3, 0.60, 0.86146588, 0.31922133, 0.22317659, 1.29282300, 1.00717700, 1},
    {2.4, 0.60, 0.98334736, 0.34325993, 0.21379372, 1.34684240, 1.05315760, 1},
    {2.5, 0.60, 1.08578332, 0.35948891, 0.20514629, 1.40000214, 1.09999786, 1},
    {2.6, 0.60, 1.17506859, 0.37082305, 0.19715562, 1.45227618, 1.14772382, 1},
    {2.7, 0.60, 1.25493924, 0.37889883, 0.18975472, 1.50367289, 1.19632711, 1},
    {2.8, 0.60, 1.32782843, 0.38472211, 0.18288555, 1.55423276, 1.24576724, 1},
    {2.9, 0.60, 1.39542311, 0.38894959, 0.17649694, 1.60402323, 1.29597677, 1},
    {3.0, 0.60, 1.45894618, 0.39202830, 0.17054328, 1.65313151, 1.34686849, 1},
    {3.1, 0.60, 1.51931329, 0.39427167, 0.16498365, 1.70165676, 1.39834324, 1},
    {3.2, 0.60, 1.57722593, 0.39590401, 0.15978122, 1.74970248, 1.45029752, 1},
    {3.3, 0.60, 1.63322992, 0.39708817, 0.15490297, 1.79737017, 1.50262983, 1},
    {3.4, 0.60, 1.68775387, 0.39794351, 0.15031931, 1.84475437, 1.55524563, 1},
    {3.5, 0.60, 1.74113581, 0.39855799, 0.14600387, 1.89193946, 1.60806054, 1},
    {3.6, 0.60, 1.79364231, 0.39899663, 0.14193319, 1.93899798, 1.66100202, 1},
    {3.7, 0.60, 1.84548298, 0.39930754, 0.13808639, 1.98599012, 1.71400988, 1},
    {3.8, 0.60, 1.89682171, 0.39952617, 0.13444496, 2.03296422, 1.76703578, 1},
    {3.9, 0.60, 1.94778568, 0.39967864, 0.13099238, 2.07995778, 1.82004222, 1},
    {4.0, 0.60, 1.99847268, 0.39978403, 0.12771397, 2.12699885, 1.87300115, 1},
    {4.1, 0.60, 2.04895718, 0.39985621, 0.12459655, 2.17410754, 1.92589246, 1},
    {4.2, 0.60, 2.09929524, 0.39990517, 0.12162834, 2.22129749, 1.97870251, 1},
    {4.3, 0.60, 2.14952859, 0.39993806, 0.11879870, 2.26857722, 2.03142278, 1},
    {4.4, 0.60, 2.19968792, 0.39995993, 0.11609803, 2.31595133, 2.08404867, 1},
    {4.5, 0.60, 2.24979553, 0.39997434, 0.11351762, 2.36342147, 2.13657853, 1},
    {4.6, 0.60, 2.29986742, 0.39998372, 0.11104955, 2.41098719, 2.18901281, 1},
    {4.7, 0.60, 2.34991493, 0.39998978, 0.10868661, 2.45864659, 2.24135341, 1},
    {4.8, 0.60, 2.39994597, 0.39999364, 0.10642219, 2.50639677, 2.29360323, 1},
    {4.9, 0.60, 2.44996605, 0.39999609, 0.10425024, 2.55423426, 2.34576574, 1},
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    {5.2, 0.60, 2.59999208, 0.39999914, 0.09823572, 2.69823199, 2.50176801, 1},
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    {5.4, 0.60, 2.69999715, 0.39999970, 0.09459735, 2.79459600, 2.60540400, 1},
    {5.5, 0.60, 2.74999832, 0.39999983, 0.09287739, 2.84287660, 2.65712340, 1},
    {5.6, 0.60, 2.79999902, 0.39999990, 0.09121886, 2.89121840, 2.70878160, 1},
    {5.7, 0.60, 2.84999943, 0.39999994, 0.08961853, 2.93961826, 2.76038174, 1},
    {5.8, 0.60, 2.89999967, 0.39999997, 0.08807338, 2.98807323, 2.81192677, 1},
    {5.9, 0.60, 2.94999981, 0.39999998, 0.08658061, 3.03658053, 2.86341947, 1},
    {6.0, 0.60, 2.99999990, 0.39999999, 0.08513760, 3.08513755, 2.91486245, 1}
  },
  {
    {2.0, 0.65, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
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    {2.9, 0.65, 1.39704291, 0.34007799, 0.14875478, 1.58001510, 1.31998490, 1},
    {3.0, 0.65, 1.46020406, 0.34283547, 0.14375418, 1.62923927, 1.37076073, 1},
    {3.1, 0.65, 1.52027857, 0.34484751, 0.13908216, 1.67797486, 1.42202514, 1},
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    {3.4, 0.65, 1.68815959, 0.34814709, 0.12674641, 1.82211008, 1.57788992, 1},
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    {4.0, 0.65, 1.99852508, 0.34980517, 0.10770023, 2.10710457, 1.89289543, 1},
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    {5.9, 0.65, 2.94999982, 0.34999998, 0.07301405, 3.02301398, 2.87698602, 1},
    {6.0, 0.65, 2.99999990, 0.34999999, 0.07179715, 3.07179711, 2.92820289, 1}
  },
  {
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    {4.0, 0.70, 1.99856520, 0.29982797, 0.08917128, 2.08868280, 1.91131720, 1},
    {4.1, 0.70, 2.04902046, 0.29988545, 0.08699555, 2.13666152, 1.96333848, 1},
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    {5.9, 0.70, 2.94999983, 0.29999999, 0.06045338, 3.01045332, 2.88954668, 1},
    {6.0, 0.70, 2.99999990, 0.29999999, 0.05944582, 3.05944579, 2.94055421, 1}
  },
  {
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    {2.3, 0.75, 0.87654496, 0.19717057, 0.12527195, 1.23089748, 1.06910252, 1},
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    {2.8, 0.75, 1.33267220, 0.23971204, 0.10282274, 1.48710054, 1.31289946, 1},
    {2.9, 0.75, 1.39922577, 0.24253756, 0.09926251, 1.53694045, 1.36305955, 1},
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    {3.8, 0.75, 1.89707585, 0.24967644, 0.07570882, 1.97489894, 1.82510106, 1},
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    {4.0, 0.75, 1.99859551, 0.24985245, 0.07192184, 2.07153074, 1.92846926, 1},
    {4.1, 0.75, 2.04904119, 0.24990174, 0.07016723, 2.11989979, 1.98010021, 1},
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    {4.4, 0.75, 2.19971313, 0.24997261, 0.06538252, 2.26530229, 2.13469771, 1},
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    {4.6, 0.75, 2.29987814, 0.24998887, 0.06253967, 2.36250557, 2.23749443, 1},
    {4.7, 0.75, 2.34992180, 0.24999301, 0.06120901, 2.41118712, 2.28881288, 1},
    {4.8, 0.75, 2.39995034, 0.24999565, 0.05993380, 2.45991990, 2.34008010, 1},
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    {5.5, 0.75, 2.74999845, 0.24999988, 0.05230583, 2.80230540, 2.69769460, 1},
    {5.6, 0.75, 2.79999909, 0.24999993, 0.05137180, 2.85137155, 2.74862845, 1},
    {5.7, 0.75, 2.84999948, 0.24999996, 0.05047054, 2.90047039, 2.79952961, 1},
    {5.8, 0.75, 2.89999970, 0.24999998, 0.04960036, 2.94960027, 2.85039973, 1},
    {5.9, 0.75, 2.94999983, 0.24999999, 0.04875967, 2.99875963, 2.90124037, 1},
    {6.0, 0.75, 2.99999990, 0.24999999, 0.04794701, 3.04794699, 2.95205301, 1}
  },
  {
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    {2.2, 0.80, 0.73143960, 0.13802120, 0.10152896, 1.16073883, 1.03926117, 1},
    {2.3, 0.80, 0.87930435, 0.15699011, 0.09710892, 1.21281590, 1.08718410, 1},
    {2.4, 0.80, 0.99741311, 0.16941871, 0.09305546, 1.26453602, 1.13546398, 1},
    {2.5, 0.80, 1.09704534, 0.17797735, 0.08932508, 1.31587559, 1.18412441, 1},
    {2.6, 0.80, 1.18410747, 0.18403573, 0.08588102, 1.36682569, 1.23317431, 1},
    {2.7, 0.80, 1.26216316, 0.18839498, 0.08269196, 1.41739228, 1.28260772, 1},
    {2.8, 0.80, 1.33355619, 0.19156218, 0.07973099, 1.46759500, 1.33240500, 1},
    {2.9, 0.80, 1.39991920, 0.19387549, 0.07697483, 1.51746477, 1.38253523, 1},
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    {3.1, 0.80, 1.52199049, 0.19680792, 0.07199828, 1.61636631, 1.48363369, 1},
    {3.2, 0.80, 1.57925511, 0.19771285, 0.06974449, 1.66548713, 1.53451287, 1},
    {3.3, 0.80, 1.63474953, 0.19837135, 0.06762804, 1.71444721, 1.58555279, 1},
    {3.4, 0.80, 1.68887839, 0.19884820, 0.06563671, 1.76328744, 1.63671256, 1},
    {3.5, 0.80, 1.74195822, 0.19919149, 0.06375969, 1.81204421, 1.68795579, 1},
    {3.6, 0.80, 1.79423686, 0.19943696, 0.06198736, 1.86074866, 1.73925134, 1},
    {3.7, 0.80, 1.84590794, 0.19961117, 0.06031114, 1.90942658, 1.79057342, 1},
    {3.8, 0.80, 1.89712206, 0.19973381, 0.05872339, 1.95809861, 1.84190139, 1},
    {3.9, 0.80, 1.94799563, 0.19981940, 0.05721723, 2.00678071, 1.89321929, 1},
    {4.0, 0.80, 1.99861784, 0.19987860, 0.05578651, 2.05548479, 1.94451521, 1},
    {4.1, 0.80, 2.04905646, 0.19991915, 0.05442566, 2.10421935, 1.99578065, 1},
    {4.2, 0.80, 2.09936242, 0.19994667, 0.05312968, 2.15299010, 2.04700990, 1},
    {4.3, 0.80, 2.14957356, 0.19996517, 0.05189402, 2.20180058, 2.09819942, 1},
    {4.4, 0.80, 2.19971771, 0.19997747, 0.05071455, 2.25065266, 2.14934734, 1},
    {4.5, 0.80, 2.24981506, 0.19998556, 0.04958752, 2.29954696, 2.20045304, 1},
    {4.6, 0.80, 2.29988009, 0.19999084, 0.04850951, 2.34848320, 2.25151680, 1},
    {4.7, 0.80, 2.34992305, 0.19999425, 0.04747738, 2.39746049, 2.30253951, 1},
    {4.8, 0.80, 2.39995114, 0.19999642, 0.04648826, 2.44647753, 2.35352247, 1},
    {4.9, 0.80, 2.44996929, 0.19999780, 0.04553951, 2.49553277, 2.40446723, 1},
    {5.0, 0.80, 2.49998090, 0.19999866, 0.04462872, 2.54462452, 2.45537548, 1},
    {5.1, 0.80, 2.54998824, 0.19999919, 0.04375364, 2.59375106, 2.50624894, 1},
    {5.2, 0.80, 2.59999284, 0.19999952, 0.04291222, 2.64291065, 2.55708935, 1},
    {5.3, 0.80, 2.64999568, 0.19999971, 0.04210256, 2.69210161, 2.60789839, 1},
    {5.4, 0.80, 2.69999742, 0.19999983, 0.04132288, 2.74132231, 2.65867769, 1},
    {5.5, 0.80, 2.74999848, 0.19999990, 0.04057156, 2.79057122, 2.70942878, 1},
    {5.6, 0.80, 2.79999911, 0.19999994, 0.03984706, 2.83984687, 2.76015313, 1},
    {5.7, 0.80, 2.84999949, 0.19999997, 0.03914799, 2.88914788, 2.81085212, 1},
    {5.8, 0.80, 2.89999971, 0.19999998, 0.03847303, 2.93847296, 2.86152704, 1},
    {5.9, 0.80, 2.94999983, 0.19999999, 0.03782094, 2.98782090, 2.91217910, 1},
    {6.0, 0.80, 2.99999991, 0.19999999, 0.03719059, 3.03719057, 2.96280943, 1}
  },
  {
    {2.0, 0.85, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.85, 0.52921303, 0.07868755, 0.07743200, 1.09252960, 1.00747040, 1},
    {2.2, 0.85, 0.73401824, 0.10282463, 0.07391092, 1.14427403, 1.05572597, 1},
    {2.3, 0.85, 0.88125553, 0.11715093, 0.07069517, 1.19578443, 1.10421557, 1},
    {2.4, 0.85, 0.99895249, 0.12659116, 0.06774673, 1.24703427, 1.15296573, 1},
    {2.5, 0.85, 1.09827719, 0.13311595, 0.06503370, 1.29800656, 1.20199344, 1},
    {2.6, 0.85, 1.18509520, 0.13774646, 0.06252912, 1.34869499, 1.25130501, 1},
    {2.7, 0.85, 1.26295173, 0.14108448, 0.06021002, 1.39910410, 1.30089590, 1},
    {2.8, 0.85, 1.33418080, 0.14351310, 0.05805670, 1.44924835, 1.35075165, 1},
    {2.9, 0.85, 1.40040905, 0.14528890, 0.05605211, 1.49915037, 1.40084963, 1},
    {3.0, 0.85, 1.46281608, 0.14658985, 0.05418146, 1.54883865, 1.45116135, 1},
    {3.1, 0.85, 1.52228177, 0.14754257, 0.05243182, 1.59834511, 1.50165489, 1},
    {3.2, 0.85, 1.57947578, 0.14823872, 0.05079184, 1.64770274, 1.55229726, 1},
    {3.3, 0.85, 1.63491472, 0.14874552, 0.04925155, 1.69694365, 1.60305635, 1},
    {3.4, 0.85, 1.68900059, 0.14911265, 0.04780210, 1.74609760, 1.65390240, 1},
    {3.5, 0.85, 1.74204757, 0.14937703, 0.04643567, 1.79519104, 1.70480896, 1},
    {3.6, 0.85, 1.79430144, 0.14956613, 0.04514532, 1.84424662, 1.75575338, 1},
    {3.7, 0.85, 1.84595410, 0.14970035, 0.04392484, 1.89328307, 1.80671693, 1},
    {3.8, 0.85, 1.89715469, 0.14979485, 0.04276868, 1.94231540, 1.85768460, 1},
    {3.9, 0.85, 1.94801843, 0.14986080, 0.04167188, 1.99135519, 1.90864481, 1},
    {4.0, 0.85, 1.99863361, 0.14990643, 0.04062997, 2.04041108, 1.95958892, 1},
    {4.1, 0.85, 2.04906725, 0.14993768, 0.03963892, 2.08948924, 2.01051076, 1},
    {4.2, 0.85, 2.09936972, 0.14995890, 0.03869508, 2.13859382, 2.06140618, 1},
    {4.3, 0.85, 2.14957845, 0.14997315, 0.03779516, 2.18772738, 2.11227262, 1},
    {4.4, 0.85, 2.19972095, 0.14998263, 0.03693616, 2.23689126, 2.16310874, 1},
    {4.5, 0.85, 2.24981718, 0.14998887, 0.03611534, 2.28608592, 2.21391408, 1},
    {4.6, 0.85, 2.29988146, 0.14999294, 0.03533022, 2.33531113, 2.26468887, 1},
    {4.7, 0.85, 2.34992394, 0.14999557, 0.03457851, 2.38456626, 2.31543374, 1},
    {4.8, 0.85, 2.39995170, 0.14999724, 0.03385812, 2.43385034, 2.36614966, 1},
    {4.9, 0.85, 2.44996964, 0.14999830, 0.03316713, 2.48316224, 2.41683776, 1},
    {5.0, 0.85, 2.49998112, 0.14999897, 0.03250379, 2.53250075, 2.46749925, 1},
    {5.1, 0.85, 2.54998838, 0.14999938, 0.03186646, 2.58186459, 2.51813541, 1},
    {5.2, 0.85, 2.59999292, 0.14999963, 0.03125364, 2.63125250, 2.56874750, 1},
    {5.3, 0.85, 2.64999573, 0.14999978, 0.03066395, 2.68066326, 2.61933674, 1},
    {5.4, 0.85, 2.69999745, 0.14999987, 0.03009610, 2.73009569, 2.66990431, 1},
    {5.5, 0.85, 2.74999850, 0.14999993, 0.02954890, 2.77954865, 2.72045135, 1},
    {5.6, 0.85, 2.79999912, 0.14999996, 0.02902124, 2.82902110, 2.77097890, 1},
    {5.7, 0.85, 2.84999949, 0.14999998, 0.02851209, 2.87851201, 2.82148799, 1},
    {5.8, 0.85, 2.89999971, 0.14999999, 0.02802051, 2.92802046, 2.87197954, 1},
    {5.9, 0.85, 2.94999983, 0.14999999, 0.02754558, 2.97754555, 2.92245445, 1},
    {6.0, 0.85, 2.99999991, 0.15000000, 0.02708649, 3.02708647, 2.97291353, 1}
  },
  {
    {2.0, 0.90, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.90, 0.53174219, 0.05196985, 0.05018313, 1.07758824, 1.02241176, 1},
    {2.2, 0.90, 0.73570255, 0.06805622, 0.04790169, 1.12871845, 1.07128155, 1},
    {2.3, 0.90, 0.88253073, 0.07768852, 0.04581839, 1.17969662, 1.12030338, 1},
    {2.4, 0.90, 0.99995864, 0.08406824, 0.04390853, 1.23050563, 1.16949437, 1},
    {2.5, 0.90, 1.09908227, 0.08849258, 0.04215132, 1.28113454, 1.21886546, 1},
    {2.6, 0.90, 1.18574063, 0.09163981, 0.04052922, 1.33157934, 1.26842066, 1},
    {2.7, 0.90, 1.26346692, 0.09391243, 0.03902727, 1.38184306, 1.31815694, 1},
    {2.8, 0.90, 1.33458880, 0.09556801, 0.03763263, 1.43193513, 1.36806487, 1},
    {2.9, 0.90, 1.40072899, 0.09677973, 0.03633423, 1.48187028, 1.41812972, 1},
    {3.0, 0.90, 1.46306420, 0.09766812, 0.03512248, 1.53166701, 1.46833299, 1},
    {3.1, 0.90, 1.52247197, 0.09831909, 0.03398899, 1.58134601, 1.51865399, 1},
    {3.2, 0.90, 1.57961986, 0.09879498, 0.03292643, 1.63092870, 1.56907130, 1},
    {3.3, 0.90, 1.63502258, 0.09914156, 0.03192835, 1.68043586, 1.61956414, 1},
    {3.4, 0.90, 1.68908038, 0.09939270, 0.03098904, 1.72988679, 1.67011321, 1},
    {3.5, 0.90, 1.74210591, 0.09957360, 0.03010346, 1.77929860, 1.72070140, 1},
    {3.6, 0.90, 1.79434361, 0.09970300, 0.02926713, 1.82868597, 1.77131403, 1},
    {3.7, 0.90, 1.84598423, 0.09979487, 0.02847603, 1.87806103, 1.82193897, 1},
    {3.8, 0.90, 1.89717598, 0.09985955, 0.02772660, 1.92743348, 1.87256652, 1},
    {3.9, 0.90, 1.94803332, 0.09990470, 0.02701561, 1.97681082, 1.92318918, 1},
    {4.0, 0.90, 1.99864390, 0.09993593, 0.02634019, 2.02619865, 1.97380135, 1},
    {4.1, 0.90, 2.04907429, 0.09995734, 0.02569773, 2.07560094, 2.02439906, 1},
    {4.2, 0.90, 2.09937448, 0.09997186, 0.02508586, 2.12502038, 2.07497962, 1},
    {4.3, 0.90, 2.14958164, 0.09998162, 0.02450246, 2.17445863, 2.12554137, 1},
    {4.4, 0.90, 2.19972306, 0.09998811, 0.02394558, 2.22391655, 2.17608345, 1},
    {4.5, 0.90, 2.24981857, 0.09999238, 0.02341345, 2.27339443, 2.22660557, 1},
    {4.6, 0.90, 2.29988236, 0.09999517, 0.02290446, 2.32289212, 2.27710788, 1},
    {4.7, 0.90, 2.34992451, 0.09999697, 0.02241713, 2.37240921, 2.32759079, 1},
    {4.8, 0.90, 2.39995206, 0.09999811, 0.02195011, 2.42194508, 2.37805492, 1},
    {4.9, 0.90, 2.44996987, 0.09999884, 0.02150215, 2.47149898, 2.42850102, 1},
    {5.0, 0.90, 2.49998126, 0.09999929, 0.02107210, 2.52107014, 2.47892986, 1},
    {5.1, 0.90, 2.54998847, 0.09999957, 0.02065892, 2.57065771, 2.52934229, 1},
    {5.2, 0.90, 2.59999297, 0.09999974, 0.02026164, 2.62026090, 2.57973910, 1},
    {5.3, 0.90, 2.64999576, 0.09999985, 0.01987934, 2.66987890, 2.63012110, 1},
    {5.4, 0.90, 2.69999747, 0.09999991, 0.01951121, 2.71951094, 2.68048906, 1},
    {5.5, 0.90, 2.74999851, 0.09999995, 0.01915646, 2.76915630, 2.73084370, 1},
    {5.6, 0.90, 2.79999913, 0.09999997, 0.01881438, 2.81881429, 2.78118571, 1},
    {5.7, 0.90, 2.84999950, 0.09999998, 0.01848430, 2.86848425, 2.83151575, 1},
    {5.8, 0.90, 2.89999971, 0.09999999, 0.01816561, 2.91816558, 2.88183442, 1},
    {5.9, 0.90, 2.94999984, 0.09999999, 0.01785771, 2.96785770, 2.93214230, 1},
    {6.0, 0.90, 2.99999991, 0.10000000, 0.01756009, 3.01756008, 2.98243992, 1}
  },
  {
    {2.0, 0.95, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 0},
    {2.1, 0.95, 0.53313676, 0.02570928, 0.02442670, 1.06343538, 1.03656462, 1},
    {2.2, 0.95, 0.73663277, 0.03376787, 0.02331635, 1.11398541, 1.08601459, 1},
    {2.3, 0.95, 0.88323525, 0.03863079, 0.02230253, 1.16446135, 1.13553865, 1},
    {2.4, 0.95, 1.00051454, 0.04186666, 0.02137316, 1.21485487, 1.18514513, 1},
    {2.5, 0.95, 1.09952705, 0.04411771, 0.02051814, 1.26516066, 1.23483934, 1},
    {2.6, 0.95, 1.18609718, 0.04572246, 0.01972888, 1.31537680, 1.28462320, 1},
    {2.7, 0.95, 1.26375149, 0.04688308, 0.01899808, 1.36550478, 1.33449522, 1},
    {2.8, 0.95, 1.33481415, 0.04772955, 0.01831948, 1.41554921, 1.38445079, 1},
    {2.9, 0.95, 1.40090568, 0.04834963, 0.01768769, 1.46551728, 1.43448272, 1},
    {3.0, 0.95, 1.46320121, 0.04880455, 0.01709803, 1.51541800, 1.48458200, 1},
    {3.1, 0.95, 1.52257700, 0.04913807, 0.01654642, 1.56526145, 1.53473855, 1},
    {3.2, 0.95, 1.57969942, 0.04938198, 0.01602930, 1.61505805, 1.58494195, 1},
    {3.3, 0.95, 1.63508212, 0.04955967, 0.01554353, 1.66481793, 1.63518207, 1},
    {3.4, 0.95, 1.68912443, 0.04968846, 0.01508634, 1.71455046, 1.68544954, 1},
    {3.5, 0.95, 1.74213812, 0.04978124, 0.01465528, 1.76426399, 1.73573601, 1},
    {3.6, 0.95, 1.79436689, 0.04984762, 0.01424817, 1.81396564, 1.78603436, 1},
    {3.7, 0.95, 1.84600087, 0.04989475, 0.01386308, 1.86366132, 1.83633868, 1},
    {3.8, 0.95, 1.89718774, 0.04992793, 0.01349825, 1.91335575, 1.88664425, 1},
    {3.9, 0.95, 1.94804153, 0.04995110, 0.01315214, 1.96305258, 1.93694742, 1},
    {4.0, 0.95, 1.99864958, 0.04996713, 0.01282333, 2.01275452, 1.98724548, 1},
    {4.1, 0.95, 2.04907817, 0.04997811, 0.01251056, 2.06246351, 2.03753649, 1},
    {4.2, 0.95, 2.09937711, 0.04998556, 0.01221269, 2.11218086, 2.08781914, 1},
    {4.3, 0.95, 2.14958340, 0.04999057, 0.01192868, 2.16190737, 2.13809263, 1},
    {4.4, 0.95, 2.19972423, 0.04999390, 0.01165757, 2.21164345, 2.18835655, 1},
    {4.5, 0.95, 2.24981933, 0.04999609, 0.01139851, 2.26138926, 2.23861074, 1},
    {4.6, 0.95, 2.29988286, 0.04999752, 0.01115072, 2.31114472, 2.28885528, 1},
    {4.7, 0.95, 2.34992483, 0.04999844, 0.01091347, 2.36090962, 2.33909038, 1},
    {4.8, 0.95, 2.39995227, 0.04999903, 0.01068610, 2.41068366, 2.38931634, 1},
    {4.9, 0.95, 2.44997000, 0.04999940, 0.01046802, 2.46046648, 2.43953352, 1},
    {5.0, 0.95, 2.49998134, 0.04999964, 0.01025866, 2.51025770, 2.48974230, 1},
    {5.1, 0.95, 2.54998851, 0.04999978, 0.01005751, 2.56005692, 2.53994308, 1},
    {5.2, 0.95, 2.59999300, 0.04999987, 0.00986410, 2.60986374, 2.59013626, 1},
    {5.3, 0.95, 2.64999578, 0.04999992, 0.00967798, 2.65967776, 2.64032224, 1},
    {5.4, 0.95, 2.69999748, 0.04999995, 0.00949876, 2.70949863, 2.69050137, 1},
    {5.5, 0.95, 2.74999851, 0.04999997, 0.00932605, 2.75932598, 2.74067402, 1},
    {5.6, 0.95, 2.79999913, 0.04999998, 0.00915952, 2.80915947, 2.79084053, 1},
    {5.7, 0.95, 2.84999950, 0.04999999, 0.00899882, 2.85899880, 2.84100120, 1},
    {5.8, 0.95, 2.89999971, 0.05000000, 0.00884367, 2.90884366, 2.89115634, 1},
    {5.9, 0.95, 2.94999984, 0.05000000, 0.00869378, 2.95869377, 2.94130623, 1},
    {6.0, 0.95, 2.99999991, 0.05000000, 0.00854888, 3.00854888, 2.99145112, 1}
  },
  {
    {2.0, 1.00, 0.00000000, 0.00000000, 0.00000000, 1.00000000, 1.00000000, 1},
    {2.1, 1.00, 0.53356933, 0.00000000, 0.00000000, 1.05000000, 1.05000000, 1},
    {2.2, 1.00, 0.73692151, 0.00000000, 0.00000000, 1.10000000, 1.10000000, 1},
    {2.3, 1.00, 0.88345397, 0.00000000, 0.00000000, 1.15000000, 1.15000000, 1},
    {2.4, 1.00, 1.00068713, 0.00000000, 0.00000000, 1.20000000, 1.20000000, 1},
    {2.5, 1.00, 1.09966513, 0.00000000, 0.00000000, 1.25000000, 1.25000000, 1},
    {2.6, 1.00, 1.18620786, 0.00000000, 0.00000000, 1.30000000, 1.30000000, 1},
    {2.7, 1.00, 1.26383982, 0.00000000, 0.00000000, 1.35000000, 1.35000000, 1},
    {2.8, 1.00, 1.33488409, 0.00000000, 0.00000000, 1.40000000, 1.40000000, 1},
    {2.9, 1.00, 1.40096052, 0.00000000, 0.00000000, 1.45000000, 1.45000000, 1},
    {3.0, 1.00, 1.46324374, 0.00000000, 0.00000000, 1.50000000, 1.50000000, 1},
    {3.1, 1.00, 1.52260960, 0.00000000, 0.00000000, 1.55000000, 1.55000000, 1},
    {3.2, 1.00, 1.57972411, 0.00000000, 0.00000000, 1.60000000, 1.60000000, 1},
    {3.3, 1.00, 1.63510061, 0.00000000, 0.00000000, 1.65000000, 1.65000000, 1},
    {3.4, 1.00, 1.68913810, 0.00000000, 0.00000000, 1.70000000, 1.70000000, 1},
    {3.5, 1.00, 1.74214811, 0.00000000, 0.00000000, 1.75000000, 1.75000000, 1},
    {3.6, 1.00, 1.79437411, 0.00000000, 0.00000000, 1.80000000, 1.80000000, 1},
    {3.7, 1.00, 1.84600603, 0.00000000, 0.00000000, 1.85000000, 1.85000000, 1},
    {3.8, 1.00, 1.89719139, 0.00000000, 0.00000000, 1.90000000, 1.90000000, 1},
    {3.9, 1.00, 1.94804408, 0.00000000, 0.00000000, 1.95000000, 1.95000000, 1},
    {4.0, 1.00, 1.99865135, 0.00000000, 0.00000000, 2.00000000, 2.00000000, 1},
    {4.1, 1.00, 2.04907938, 0.00000000, 0.00000000, 2.05000000, 2.05000000, 1},
    {4.2, 1.00, 2.09937793, 0.00000000, 0.00000000, 2.10000000, 2.10000000, 1},
    {4.3, 1.00, 2.14958394, 0.00000000, 0.00000000, 2.15000000, 2.15000000, 1},
    {4.4, 1.00, 2.19972459, 0.00000000, 0.00000000, 2.20000000, 2.20000000, 1},
    {4.5, 1.00, 2.24981957, 0.00000000, 0.00000000, 2.25000000, 2.25000000, 1},
    {4.6, 1.00, 2.29988301, 0.00000000, 0.00000000, 2.30000000, 2.30000000, 1},
    {4.7, 1.00, 2.34992493, 0.00000000, 0.00000000, 2.35000000, 2.35000000, 1},
    {4.8, 1.00, 2.39995233, 0.00000000, 0.00000000, 2.40000000, 2.40000000, 1},
    {4.9, 1.00, 2.44997004, 0.00000000, 0.00000000, 2.45000000, 2.45000000, 1},
    {5.0, 1.00, 2.49998137, 0.00000000, 0.00000000, 2.50000000, 2.50000000, 1},
    {5.1, 1.00, 2.54998853, 0.00000000, 0.00000000, 2.55000000, 2.55000000, 1},
    {5.2, 1.00, 2.59999301, 0.00000000, 0.00000000, 2.60000000, 2.60000000, 1},
    {5.3, 1.00, 2.64999579, 0.00000000, 0.00000000, 2.65000000, 2.65000000, 1},
    {5.4, 1.00, 2.69999749, 0.00000000, 0.00000000, 2.70000000, 2.70000000, 1},
    {5.5, 1.00, 2.74999852, 0.00000000, 0.00000000, 2.75000000, 2.75000000, 1},
    {5.6, 1.00, 2.79999913, 0.00000000, 0.00000000, 2.80000000, 2.80000000, 1},
    {5.7, 1.00, 2.84999950, 0.00000000, 0.00000000, 2.85000000, 2.85000000, 1},
    {5.8, 1.00, 2.89999971, 0.00000000, 0.00000000, 2.90000000, 2.90000000, 1},
    {5.9, 1.00, 2.94999984, 0.00000000, 0.00000000, 2.95000000, 2.95000000, 1},
    {6.0, 1.00, 2.99999991, 0.00000000, 0.00000000, 3.00000000, 3.00000000, 1}
  }
};



/* Return the correct line width w and asymmetry h, and a line position
   correction correct for a line with extracted width w_est and extracted
   gradient ratio r_est for a given sigma.  Furthermore, return the line width
   on the weak and strong side of the line.  These values are obtained by
   bilinear interpolation from the table ctable. */
bool line_corrections(
  double sigma,
  double w_est,
  double r_est,
  double *w,
  double *h,
  double *correct,
  double *w_strong,
  double *w_weak
)
{
  long   i_we,i_re;
  bool   is_valid;
  double a,b;

  w_est = w_est/sigma;
  if (w_est < 2 || w_est > 6 || r_est < 0 || r_est > 1) {
    *w = 0;
    *h = 0;
    *correct = 0;
    *w_strong = 0;
    *w_weak = 0;
    return 1;
  }
  i_we = floor((w_est-2)*10);
  i_re = floor(r_est*20);
  if (i_we == 40)
    i_we = 39;
  if (i_re == 20)
    i_re = 19;
  is_valid = ctable[i_re][i_we].is_valid && ctable[i_re][i_we+1].is_valid &&
             ctable[i_re+1][i_we].is_valid && ctable[i_re+1][i_we+1].is_valid;
  a = (w_est-2)*10-i_we;
  b = r_est*20-i_re;
  *w = BILINEAR(a,b,w)*sigma;
  *h = BILINEAR(a,b,h);
  *correct = BILINEAR(a,b,correction)*sigma;
  *w_strong = BILINEAR(a,b,w_strong)*sigma;
  *w_weak = BILINEAR(a,b,w_weak)*sigma;
  return !is_valid;
}
